AUTOMATED TESTING OF ACCELEROMETER TRANSVERSE SENSITIVITY
Jeffrey J. Dosch David M. Lally R&D Group Leader Engineering Vice President
PCB Piezotronics Depew NY 14043
ABSTRACT The trend in modal testing is for increasingly large channel counts and the consequent demand for lower cost sensors. A new system for automated testing of accelerometer The challenge to the sensor manufacturer is to reduce the transverse sensitivity has been designed and implemented sensor cost without sacrificing quality and sensor accuracy. at PCB Piezotronics. This paper describes the transverse Because of the costs involved in final calibration, rather test system theory, construction, and operation. Transverse than testing on a 100% basis, some sensor manufacturers sensitivities obtained from the automated system and have addressed the cost challenge by statistical sampling of sensitivities obtained by the manual method described in some of their final tests. Where feasible, PCB Piezotronics ISO 5347-11:1993 were found to agree to within the stated has addressed the challenge in a different way and that is uncertainty of 0.3%. to automate the final calibration testing, and thus allow cost- effective final calibration of each sensor manufactured. NOMENCLATURE This paper describes a new automated system for testing of accelerometer transverse sensitivity. The system uses a ai linear acceleration [g] resonant beam to generate uniform motion in the transverse plane. The beam motion is controlled and data is acquired α rotational acceleration [radian/s2] i via computer-based acquisition and control. Compared to
Si linear sensitivity [mV/g] the manual method used previously, the new approach has Ψ 2 been found to provide more accurate and consistent i rotational acceleration [mV/rad/ s ] calibration in the production environment. SUT sensor under test THEORY vo SUT output [Volts] ϕ Interferometer phase [radian] Ideally, an accelerometer will respond only to motion along its sensing axis. In the non-ideal world an accelerometer S sensitivity [mV/g] may respond to axial acceleration in a direction 2 g acceleration constant [9.80665 m/s ] perpendicular to the main sensing axis and to rotational ω acceleration. Consider the accelerometer with the desired c excitation frequency [radian/s] Re( ) real part of ( ) sensing axis oriented in the z direction (Figure 1) and Im( ) imaginary part of ( ) subject to both linear and rotational acceleration. Output ( )* complex conjugate of ( ) from the sensor will be equal to: subscripts: a x,y,z coordinate axes x t transverse direction a y a z v = []S S S Ψ Ψ Ψ (1) INTRODUCTION o x y z x y z α x A number of final calibration tests are performed by an α accelerometer manufacturer to ensure the quality and y accuracy of the sensor used by the test engineer. Final α z calibration of an accelerometer for “test and measurement” applications may include testing of sensor sensitivity, Where a and α are the linear and rotational acceleration frequency response, time constant, resonant frequency, i i Ψ and transverse sensitivity. components S i and i are the accelerometer’s sensitivity to these accelerations. For most piezoelectric Improved signal resolution can be obtained by using Fourier accelerometers the rotational sensitivity, Ψ , is small and domain signal processing. The improved resolution is i especially useful when testing accelerometers with low can be ignored. In such instances, only linear acceleration sensitivity such as shock accelerometers that may have components contribute to sensor output: main axis sensitivities as small as 0.05 mV/g. ax A digital Fourier transform is applied to the acquired signals. = [] The spectral components of the SUT and x-y reference vo S x S y S z a y (2) sensors evaluated at the excitation frequency ω are the a c z complex quantities: For the sensor with sensing oriented along the z-axis, the ω = () A ( j ) FFT a (t) ω =ω (10) x c x c maximum transverse sensitivity has a magnitude equal to St ω = () (Figure 1): Ay ( j c ) FFT ay (t) ω =ω (11) c 2 2 ω = () = + V ( j ) FFT v (t) ω =ω (12) St S x S y (3) o c o c
The transverse sensitivity is usually expressed as a The SUT output that is in-phase with the x and the y percentage of the main axis sensitivity: reference accelerometers is respectively: ∗ St A Tranverse(%) =100 ⋅ (4) V = ReV x (13) S x o z Ax Typical values of transverse sensitivity are: less than 2% for ∗ Ay piezoelectric quartz accelerometers and less than 5% for V = Re V (14) piezoceramic accelerometers. y o Ay The calibrator described in this paper generates rectilinear ω The cross sensitivities in the x and the y directions are: acceleration in the x-y plane at a frequency c . The motion is controlled such that acceleration components V = x along the x and y axis are in phase quadrature (shifted in S x (15) phase by 90 degrees): Ax
= ω Vy a x (t) X sin( c t) (5) = S y (16) Ay a (t) = Y cos(ω t) (6) y c Given the above cross sensitivities in the x and y directions, In the general case equations (5) and (6) describe elliptical the maximum transverse sensitivity magnitude and direction motion in x-y plane; if X = Y, then a circle is described. In is calculated: the automated test system, acceleration components a x = 2 + 2 St S x S y (17) and a y are measured with reference accelerometers. Acceleration magnitude and direction determined at any S θ = −1 y time t is: t tan (18) S x = 2 + 2 at (t) ax a y (7)
AUTOMATED TRANSVERSE TESTER a −1 y θ (t) = tan (8) The automated transverse test system consists of a a resonant beam, x and y reference accelerometers, x independent x and y exciters to generate acceleration in the Maximum transverse sensitivity of the sensor under test x-y plane, and personal computer based acquisition and control (Figures 2 and 3). The computer acquires the SUT (SUT) is then determined from the SUT output, vo (t) , and Eq (7): and x and y reference signals. The computer also controls the motion in the x-y plane, generating near circular motion v (t) according to equations (5) and (6) with X =Y, while = o St max (9) maintaining phase quadrature. Transverse sensitivity is a (t) calculated from the acquired signals using Eqs. (10) t through (18). Eq (9) describes a time domain method for calculating the maximum transverse sensitivity and assumes phase The resonant beam was designed to provide rectilinear quadrature of the x and y reference accelerometers. motion in the x-y plane, with negligible motion in the z direction and minimal rotational acceleration. The measurement error due to rotational acceleration depends CONCLUSION on both the accelerometer’s rotational sensitivity (which is generally small) and the level of rotational acceleration of A new automated system for testing of accelerometer the exciter. transverse sensitivity has been implemented at PCB Piezotronics. Compared to the manual method of testing An estimated uncertainty was calculated for the automated described in ISO 5347-11:1993, the automated system test system according to procedures described in reference provides cost-effectiveness, accuracy, and consistency in [1]. Influences contributing to the calculated uncertainty the production environment. Additionally, the system can include: exciter rotational acceleration, accelerometer measure transverse output of low sensitivity sensors such sensitivity to rotation, residual z-axis motion, measurement as shock accelerometers that may have axial sensitivity as noise, and random testing errors. For sensors with low as 0.05 mV/g. transverse sensitivities ranging from 0% to 5%, an expanded measurement uncertainty of 0.3% (additive) is typical. REFERENCES ISO 5347-11:1993 [2] describes a standard method for [1] NIST Technical Note 1297, “Guidelines for Evaluating testing of accelerometer transverse sensitivity. The SUT is and Expressing the Uncertainty of NIST Measurement mounted to a shaker such that the main sensing axis is Results,” 1994. perpendicular to the shaker motion (Figure 4). Using a special fixture the sensor is rotated about the sensing axis [2] ISO 5347-11:1993. “Methods for the calibration of and measurements taken until the direction and magnitude vibration and shock pick-ups -- Part 11: Testing of of largest transverse acceleration is found. transverse vibration sensitivity,” 1993 To validate the operation of the automated transverse tester, a number of sensors were tested by the method of ISO 5347-11:1993 and with the new system. A random sampling of the test results is given in Table 1. FIGURES Characteristics of the sensors tested are provided in Table
2. From Table 1 it can be observed that the transverse sensitivities measured by the two methods were found to agree to within the expanded uncertainty of the automated z transverse test system (expanded uncertainty = 0.3%). S Table 1: Comparison of two methods. z Transverse Sensitivity S Sensor ISO 5347 New Difference [2] method 353B17 0.9% 1% +0.1% S/N C48274 353B17 0.3% 0.4% +0.1% S/N C48286 353B33 0.9% 0.8% -0.1% Sy y S/N 60048 353B33 0.6% 0.5% +0.1% S S/N 60047 x 353B04 0.6% 0.7% +0.1% St S/N C44363 353B04 0.5% 0.4% -0.1% S/N C44364 x θ
Table 2: Sensor Characteristics. Sensitivity Mass Figure 1: Accelerometer sensitivity vector S, and (mV/g) (grams) components along x, y, and z axes. 353B17 10 2.9 353B33 100 27.0 353B04 10 10.5
y FIXTURE SUT DIRECTION OF TOP VIEW TRANSVERSE EXCITATION x θ
SUT z Y ACCELEROMETER SHAKER ARMATURE
X ACCELEROMETER
SIDE VIEW Y EXCITER BEAM
SIGNAL
AMPLIFIER CONDITIONER
BASE
X EXCITER
COMPUTER A/D AND D/A SHAKER
MOTION Figure 2: System for automated testing of accelerometer transverse sensitivity. Figure 4: Method for testing transverse sensitivity using a vibration shaker.
Figure 3: Resonant beam with reference accelerometers and sensor under test.